From the thread:
Science Museum....yep, good recommendation but be prepared for loads of kids. Most museums are free. The Tate Modern is impressive but you probably won't have time and the Science Museum is more fun
Trocadero - more touristy than it was but may be worth visiting still. Has Laser tag and a gaming arcade which was quite fun last time I visited but that was a while ago.
Londoners cross roads whenever they feel like it...we're not that bothered about traffic lights or pedestrian crossings. They're just guidance.
Madame Tussauds - don't know why people bother. It's expensive and I don't see how it is any different from any waxworks anywhere
Agree with London Eye - good thing to do but maybe expensive for what it is.
Avenue Q - seen it. It's a good show
Camden - worth visiting. Loads of interesting stalls and shops. This place is great
http://shop.cyberdog.net/ Unfortunately it's got more touristy. Not many oldskool ravers anymore.
New Year - as well as the age issue, pubs and clubs at New Year are overpriced and often you have to pay to get in on New Year's Eve, it's easy to get ripped off. Outside New Year's Eve you won't have a problem getting into pubs. You may be better off soaking up the vibe just out and about in Trafalgar Square and by the river, watching the fireworks, and joining in the crowd as it counts down the year with Big Ben. Public transport is free and lasts all night and everyone is out to just enjoy themselves. Keep an eye out for anything fun that might be happening and go with the flow.
http://www.visitlondon.com/things-to-do/event/27002385-mayors-new-years-eve-fireworks-at-edf-energy-london-eye(one of the best New Year's Eve I had was when a group of us just went to Trafalgar Square with no plans, saw the New Year in, heard there was a party happening in Brixton, tried to drive there in my van, got caught in traffic going down Charing Cross Road and found ourselves starting an impromptu rave with the van as a slowly moving sound system surrounded by dancing crowds...don't think I'd ever had so many New Year kisses

)
On New's Day there is the London's New Year's Day Parade
Why Burger King?